### SIMPLIFYING ALGEBRAIC EXPRESSIONS

```SIMPLIFYING ALGEBRAIC
EXPRESSIONS
•MULTIPLYING LIKE TERMS
•SIMPLIFYING EXPRESSIONS
•REPLACING LETTERS WITH NUMBERS TO
GET A VALUE FOR AN EXPRESSION
•USING FORMULAS
•REMOVING BRACKETS
3+3+3+3
4 X3
This gives the
a+ a+a +a
4a
Can be written in the shorter form
Meaning that we have
4 bundles of 3’s
VALUE
12
Can be written in the shorter form
We cannot give a value for 4a until we
are given a value for a
If
a=7
4a
=
Then by replacing a with 7
4 x(7)
= 28
So a value for the expression 4a
when a = 7 is
28
Some examples
Simplify the following expressions
3a + 2a
= a+a+a
+
Combine all the
a’s together to
get one term
a+a
= 5a
5b – 2b
= b+b+b+b+b
= 3b
-
b+b
Take 2 b’s away
from the 5 b’s
Simplifying expressions with numbers
and different letters
Simplify
3a + 2b + 5a + 3b + 7
3a + 5a +
8a
+
2b + 3b
5b
8a + 5b +7
+
+
7
7
WE can
subtract like
terms to
each other
Multiplying like terms
Can be written in the shorter form
2 X 2 X 2 X 2 X2
This means that 2 is
multiplied by itself 5 times
25
This gives a
value
aXaXaXaXa
a5
32
Can be written in the shorter form
We cannot get a value for a5 until
we are given a value for a
If a = 7 then
a5
=
75
=16807
So a value for the expression
when a = 7
is
16807
a5
Some examples
Simplify the following expressions
3a x a
=3xaxaxa x a
=
3b x 2b
We now have 3 times a
multiplied by itself 4
times
3 a4
=3x2
=6
=6
x
x
b2
bxb
b2
Multiply the numbers
together and multiply
the letters together
Write product
without
multiplication sign
Examples with numbers and letters
3b2 X 4b3
3X4
12
12
b2X b3
X
X
X
bXb X bXbXb
b5
Multiply the
numbers together
b2X b3 = b2+3
powers
=b5
Simplify
REMEMBER
r = r1
4r x 6s x r2 x s3
= 4x6
x
x
s x s3
Multiply similar letters
Multiply the
numbers together
24
r x r2
x
r1+2
=24 r3s4
x
s1+3
When we multiply letters and
numbers first put the numbers next
the letters in alphabetical order and
we do not need the X sign
Order of operations
5+2x3
=
11
Not 21
In mathematics we have rules
Multiplication or division is calculated before
2xa +5
6–2xb
Is simplified to
Is simplified to
2a + 5
6-2b
Have you got it yet ?
Simplify the following
1. 2a + 3a
2. 3a + 4b + 2a + 5b
5a
5a + 9b
8 . 3m + 2m + 7
9. 6j – 3j + j
5m+ 7
4j
b4
10. 3s x 4s x 6
72b2
4. b x b x c x c x c
b2c3
11. 3 x s + 7
3s+7
5. 4b2 x 5b3
20b5
12. 6 + 3 x d
6+3d
6. 3c x 4b
12bc
13 . 10n – 2 x 3n 4n
7. 2 c 4 + 3c4
5c4
14. 8b – 3 x b2
3. b x b x b x b
8b –. 3 b2
Finding values for expressions
Find a value for the expression
3b =
3b
when b =7
3 x (7) = 21
Take out b and
replace it with 7
Put 7 inside a
bracket
21 is the value of
the expression
Find a value for the expression 3c + b
when c = 2 and b = 5
3c + b
= 3 x (2) + ( 5)
Replace c with 2
and
b with 5
= 6+5
= 11
11 is the value of the
expression
Find a value for the expressions
a) pq
b) 2p + q
c) 5pq +2p
e) 3 ( p + 2q )
f) ( p + q ) 2
when
p = 3 and q = 7
a)
pq
b) 2p + q
= (3) x (7)
= 2 x ( 3) + ( 7 )
= 21
=
6
= 13
d) q2 - p2
= (7)2 - (3)2
= 49 - 9
= 40
+ 7
e) 3 ( p + 2q )
= 3 ( (7) + 2x(3) )
= 3( 7 + 6)
= 3 x 13 = 39
d) q2 - p2 when
c) 3pq + 2p
= 3x(3)x(7)+2x(3)
= 63 + 6
= 69
f)
(q-p)2
= ( (7) – (3) ) 2
=(4)2
= 16
```